Step 1: Understanding strain energy.
Strain energy is the energy stored in a body due to deformation caused by an applied load.
Step 2: Defining proof resilience.
Proof resilience is defined as the maximum strain energy that a body can store without undergoing permanent deformation, i.e., within the elastic limit.
Step 3: Eliminating incorrect options.
Impact energy refers to energy due to sudden loading.
Proof stress is the stress corresponding to a specified permanent strain.
Modulus of resilience is the proof resilience per unit volume.
Step 4: Conclusion.
Therefore, the strain energy stored without permanent distortion is called proof resilience.